Question

Completely factor the expression 7x² + 21x.

which one is it?
3 (x² + 7)
(2x + 7) (x + 3)
2 (7x + 21)
7x (x + 3)​

Answer 1

7x (x + 3) is the correct answer

Answer 2

Hii!

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`\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}}}\circ\leftharpoonup`

Choice [D] - 7x(x+3)

`\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation}}}\circ\leftharpoonup`

Note that both terms have something in common.

This "something" is called the greatest common factor (g.c.f.)

In this example the g.c.f. is 7x. So we factor it out by dividing both terms of the expression by 7x.

`\twoheadrightarrow\sf 7x^2/7x=x`

`\twoheadrightarrow\sf 21x/7x=3`

`\bullet` Put the terms together, with a plus sign in between since they are both positive

`\twoheadrightarrow\sf x+3`

`\bullet` Put parentheses around x+3

`\twoheadrightarrow\sf (x+3)`

`\bullet` Put 7x outside the parentheses

`\twoheadrightarrow\sf 7x(x+3)`

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Hope that this helped! Best wishes.

`\stackrel\star{\textsl{Reach far. Aim high. Dream big.}}`

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